If you are attacking a province containing iron mine and win the conflict by 5 if you played fallen in battle then could the defending crab player use that iron mine to save the character fib is trying to kill?

Yes, because you win the conflict in step 3.2.3, after comparing skill values, and use FiB as a reaction in that step. Then, the defending player uses Iron Mine as a interrupt to your FiB.

After resolving this, you go to step 3.2.4 (apply unopposed), and then to step 3.2.5 (Break province), which is when you can choose to discard the card in that province if you broke it. Which in this case will be the facedown card that replaced Iron Mine.